The matrix 0& 1 1& 0 is the matrix reflection in the line… - Vidyadip

MCQ

The matrix $\begin{bmatrix}0&\text{amp; }1\\1&\text{amp; }0\end{bmatrix}$ is the matrix reflection in the line :

A
$x = 1$
B
$x + y = 1$
C
$y = 1$
✓
$x = y$

✓

Answer

Correct option: D.

$x = y$

We know that the reflection matrix through a line $\text{y}=\text{mx}$ making an $\angle \theta$ with $x -$ axis is given as.
$\begin{bmatrix} \cos { 2\theta }&\text{amp;}\sin { 2\theta } \\ \sin { 2\theta } &\text{amp;} -\cos { 2\theta }\end{bmatrix}$
Given transformation matrix is $\begin{bmatrix}0&\text{amp; }1\\1&\text{amp; }0\end{bmatrix}$
$\Rightarrow\cos2\theta=0\sin2\theta=1$
$\Rightarrow 2\theta ={90}^\circ$
$\Rightarrow \theta={45}^\circ$
$\Rightarrow \tan \theta=1$
Hence, the line of reflection is $\text{y}=\text{x}$

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